Question Number 187529 by sciencestudentW last updated on 18/Feb/23 $$\int{x}^{\mathrm{2}} \centerdot{sin}^{−\mathrm{1}} \left({x}\right){dx}=? \\ $$ Answered by Humble last updated on 18/Feb/23 $$\int\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{arcsin}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}} \\ $$$$\boldsymbol{{I}}{BP}…
Question Number 187531 by sciencestudentW last updated on 18/Feb/23 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$ Answered by a.lgnaoui last updated on 18/Feb/23 $${posons}\:\:\:{t}={e}^{{x}} \:\:{x}={lnt}\:\:\:{dx}=\frac{{dt}}{{t}}…
Question Number 187528 by sciencestudentW last updated on 18/Feb/23 $$\underset{\frac{\mathrm{9}\pi}{\mathrm{2}}} {\overset{\frac{\mathrm{7}\pi}{\mathrm{1}.\mathrm{5}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{sinx}}}=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−\mathrm{sin}{x}}} \\ $$$$\:\:=\int\frac{{dx}}{\mid\mathrm{cos}\frac{{x}}{\mathrm{2}}−\mathrm{sin}\frac{{x}}{\mathrm{2}}\mid}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\mathrm{cos}\left(\frac{{x}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)} \\…
Question Number 187530 by sciencestudentW last updated on 18/Feb/23 $$\int\frac{{dx}}{\:\sqrt{{a}^{\mathrm{2}} +{be}^{{cx}} }}=? \\ $$ Answered by anurup last updated on 18/Feb/23 $${a}^{\mathrm{2}} +{be}^{{cx}} ={t}^{\mathrm{2}} \\…
Question Number 187526 by sciencestudentW last updated on 18/Feb/23 $$\int\frac{{dx}}{{cscx}−\mathrm{1}}=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $${I}=\int\frac{{dx}}{\mathrm{cosec}{x}−\mathrm{1}} \\ $$$$\:\:=\int\frac{\mathrm{sin}{x}}{\mathrm{1}−\mathrm{sin}{x}}{dx}=\int\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{sin}{x}}−\mathrm{1}\right){dx} \\ $$$$\:\:=\int\frac{\mathrm{1}+\mathrm{sin}{x}}{\mathrm{cos}^{\mathrm{2}} {x}}{dx}−{x}=\mathrm{tan}{x}+\frac{\mathrm{1}}{\mathrm{cos}{x}}−{x}+{C}…
Question Number 121972 by Lordose last updated on 13/Nov/20 $$\int_{\mathrm{0}} ^{\:\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{cos}\left(\mathrm{5x}\right)\mathrm{dx} \\ $$ Answered by Bird last updated on 13/Nov/20 $$\mathrm{2}{I}=\int_{−\infty} ^{+\infty}…
Question Number 121965 by bemath last updated on 13/Nov/20 $$\:\:\:\:\:\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\:\frac{\ell{n}\:\left({x}\right)}{\:\sqrt{{x}}}\:{dx}\:? \\ $$ Answered by bemath last updated on 13/Nov/20 $$\:\underset{\mathrm{4}} {\overset{\mathrm{9}} {\int}}\:\frac{\ell{n}\left({x}\right)}{\:\sqrt{{x}}}\:{dx}\:=\:\underset{\mathrm{2}} {\overset{\mathrm{3}}…
Question Number 121962 by bemath last updated on 13/Nov/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt[{\mathrm{3}\:}]{{x}^{\mathrm{2}} −{x}^{\mathrm{3}} }}\:?\: \\ $$ Answered by MJS_new last updated on 13/Nov/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 121928 by Dwaipayan Shikari last updated on 12/Nov/20 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{12}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{12}{n}+\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{12}{n}+\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{12}{n}+\mathrm{11}}\right) \\ $$$$ \\ $$$${Problem}\:{source}\::\:{Brilliant}.{Org} \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 56383 by Tawa1 last updated on 15/Mar/19 Commented by Tawa1 last updated on 16/Mar/19 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$ Commented by maxmathsup by imad last…